A direct impedance tomography algorithm for locating small inhomogeneities

Numerische Mathematik

Volumn 93, Issue 4, 2003, Pages 635-654

  Brühl, Martin ^a   Hanke, Martin ^a   Vogelius, Michael S ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038594506     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110200409     Document Type: Review

References (16)

1. H. Ammari, S. Moskow, M. S. Vogelius: Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. To appear in ESAIM Control Optim. Calc. Var.
2. H. Ammari, M. S. Vogelius, D. Volkov: Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations. J. Math. Pures Appl., IX. Ser 80, 769-814 (2001)
3. M. Brühl: Explicit characterization of inclusions in electrical impedance tomography. SIAM J. Math. Anal., 32, 1327-1341 (2001)
4. M. Brühl, M. Hanke: Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Probl., 16, 1029-1042 (2000)
5. D. J. Cedio-Fengya, S. Moskow, M. S. Vogelius: Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Probl., 14, 553-595 (1998)
6. M. Cheney: The linear sampling method and the MUSIC algorithm. Inverse Probl., 17, 591-595 (2001)
7. M. Cheney, D. Isaacson, J. C. Newell: Electrical impedance tomography. SIAM Rev., 41, 85-101 (1999)
8. A. J. Devaney: Super-resolution processing of multi-static data using time reversal and MUSIC. To appear in J. Acoust. Soc. Am.
9. G. B. Folland: Introduction to Partial Differential Equations. Princeton University Press, Princeton, 1976
10. A. Friedman, M. Vogelius: Identification of small inhomogenities of extreme conductivity by boundary measurements: a theorem on continuous dependence. Arch. Ration. Mech. Anal., 105, 299-326 (1989)
11. D. G. Gisser, D. Isaacson, J. C. Newell: Electric current computed tomography and eigenvalues. SIAM J. Appl. Math., 50, 1623-1634 (1990)
12. T. Kato: Perturbation Theory for Linear Operators. Springer, Berlin, 1966
13. A. Kirsch: Characterization of the shape of the scattering obstacle using the spectral data of the far field operator. Inverse Probl., 14, 1489-1512 (1998)
14. C. Miranda: Partial Differential Equations of Elliptic Type. Springer, Berlin, 2nd ed., (1970)
15. A. B. Movchan, S. K. Serkov: The Pólya-Szegö matrices in asymptotic models of dilute composites. Eur. J. Appl. Math., 8, 595-621 (1997)
16. M. S. Vogelius, D. Volkov: Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. M2AN Math. Model. Numer. Anal., 34, 723-748 (2000)